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Abstract
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In this paper it is shown that
the problem of solving the triple series equations of the first kind
| ∑
n=0∞A
nΓ(α + 1 + n)Ln(α;x) | = 0, 0 ≦ x < a, | (1)
| | ∑
n=0∞A
nΓ(α + β + n)Ln(α;x) | = f(x), a < x < b, | (2)
| | ∑
n=0∞A
nΓ(α + 1 + n)Ln(α;x) | = 0, b < x < ∞, | (3) |
and the triple series equations of the second kind
| ∑
n=0∞B
nΓ(α + β + n)Ln(α;x) | = g(x), 0 ≦ x < a, | (4)
| | ∑
n=0∞B
nΓ(α + 1 + n)Ln(α;x) | = 0, a < x < b, | (5)
| | ∑
n=0∞B
nΓ(α + β + n)Ln(α;x) | = h(x), b < x < ∞, | (6) |
where α + β > 0, 0 < β < 1, Ln(α;x) = Lnα(x) is the Laguerre polynomial and
f(x), g(x) and h(x) | |
